Development of calculation formulas for cylinder wall ...

Development of calculation formulas for cylinder

wall thickness

Technical Information: TI 002

Issue Date: 2018-01-02

Rev. No. 0

Page 1 of 10

Technical Information (TI)

No: TI 002

Technical Group for seamless gas

cylinders

Development of calculation formulae for cylinder

wall thickness

Table of content

Issue: 2018-01-02

Rev. No. 0

Page

1. Purpose

3

2. Scope

3

3. Introduction

3

4. Historical background and evaluation of design formulae by

ISO/C58/SC3

4

5. Conclusion

6

6. References

7

ANNEX A

Calculation examples for cylinders in accordance with the Bach

Clavarino formula, the Mean Diameter formula and the Lam¨¦ von

Mises formula

8 - 10

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Technical Information (TI)

No: TI 002

Technical Group for seamless gas

cylinders

Development of calculation formulae for cylinder

wall thickness

Issue: 2018-01-02

Rev. No. 0

1. Purpose

The purpose of this document is to explain the historical background and differences

of the formulae used to calculate the minimum design wall thickness of seamless

steel and aluminium alloy cylinders.

2. Scope

The scope of this document is limited to the following formulae which are used to

calculate the minimum design wall thickness of seamless steel and aluminium alloy

cylinders:

? Bach Clavarino formula

? Mean diameter formula

? Lam¨¦ von Mises formula

3. Introduction

Over the years three main formulae have been used to calculate the sidewall thickness

of gas cylinders. These are:

a) the Bach Clavarino formula (e.g. used in DOT regulations)

[

(

(

)]

¡Ì

)

b) the Mean Diameter formula (e.g. used in EEC Directives 84/525/EEC and

84/526/EEC, ISO4705 and many other national standards/codes/regulations in

Europe)

Page 3 of 10

Technical Information (TI)

No: TI 002

Technical Group for seamless gas

cylinders

Development of calculation formulae for cylinder

wall thickness

Issue: 2018-01-02

Rev. No. 0

c) the Lam¨¦ von Mises formula (e.g. used in new ISO designs)

(

¡Ì

¡Ì

where the value of F is the lesser of

)

?

or 0,85.

¡°Ref. ISO 9809-1¡±

Whereby the symbols have the following meaning:

a

D

d

Ph

Reg

Rmg

F

S

calculated minimum wall thickness in mm (in inches for the Bach Clavarino

formula)

outside diameter of the cylinder in mm (in inches for the Bach Clavarino

formula )

inside diameter of the cylinder in inches

hydraulic test pressure in bar (in psi for the Bach Clavarino formula)

minimum guaranteed value of yield stress in MPa

minimum guaranteed value of tensile strength in MPa

design stress factor is the ratio of equivalent wall stress and test pressure to

guaranteed minimum yield stress

wall stress in psi

4. Historical background and evaluation of design formulae by ISO/TC58/SC3

Many years ago, a Technical Committee of the International Standardisation

Organisation ISO/TC58 was founded (1947) to develop international standards in the

field of gas cylinders. This committee created a Sub-Committee ISO/TC58/SC3 which is

responsible for the development of cylinder design standards.

The first ISO standard for seamless steel gas cylinders was published in 1983, namely

ISO 4705. This standard used the Mean Diameter formula to calculate wall thickness.

However, it was evident that two other formulae are also used worldwide to calculate

wall thickness. Indeed, each formula results in slightly different wall thicknesses. As a

consequence, ISO/TC58/SC3 established a working group WG-8 in 1981 (under the

leadership of BSI) to investigate which of the three formulae most accurately reflects

the actual stresses in the side walls of gas cylinders, see figure 1.

Page 4 of 10

Technical Information (TI)

No: TI 002

Technical Group for seamless gas

cylinders

Development of calculation formulae for cylinder

wall thickness

Issue: 2018-01-02

Rev. No. 0

Cylinders with exactly defined wall thicknesses and mechanical properties, were

produced and strain measurements were taken at increasing applied pressures up to

and beyond test pressure to cause ¡°elastic failure¡±.

The research project can be summarized as follows:

The general conclusion was that over the range of materials and cross sectional

geometries investigated, the Lam¨¦ von Mises formulae were able to most closely

predict elastic failure, and that this formula is therefore the preferred one for deriving

required wall thickness of gas cylinders in terms of equivalent stress distribution.

The Bach Clavarino formula tends to overestimate internal pressure causing elastic

failure, and the mean diameter formula tends to underestimate pressure to promote

elastic failure for thin walls and overestimate for thick walls.

In more detail the outcome showed that gas cylinders can be

categorized as:

- Thin-walled cylinders (Dexternal / Dinternal around 1,06), are best calculated by the

Lam¨¦ von Mises formula and is most applicable.

- Thick-walled cylinders with a diameter ratio Dexternal / Dinternal around 1,16 ¨C 1,20 like

aluminium alloy or normalized mild steel cylinders, are best calculated by either the

Mean Diameter or Lam¨¦ von Mises formula..

- Whereas, the Bach Clavarino formula results in slightly underestimated wall

thicknesses (see graph below).

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